Deep-Diving Submarine Hydrodynamics 337 
Flat Ends: PLS Le, = Eine ea 0 
DL, + yD? an 
Cat, a nDied aot yRikae 
For all configurations the wetted surface can be expressed in terms of the volume 
V, Cp, Cs, L/D as follows: 
e 
1/3 2/3 
5) 
S.C. fin 
Cursory inspection of all of the preceding relationships will indicate the wisdom of 
leaving them in the parametric form in which they are expressed. Since both Cp and Cs 
are expressed in terms of L,’, it could be eliminated as a parameter and the wetted surface 
could then be expressed directly as a function of C, and L/D for any given volume. The 
resulting expressions would, however, be extremely ponderous. 
DISCUSSION 
E. C. Tupper (Admiralty Experiment Works) 
My remarks are not so much a question directed to the author, but rather a request to 
him that he might study certain problems associated with the control of this submarine when 
it is in operation. I think it is desirable to go a little into the background of the problem to 
bring out the points I wish to make. There are two points of great interest in the control 
of an underwater body in the vertical plane. So as not to become involved in any problems 
of nomenclature, | will call these points A and 3. 
Point A is a fixed point in the submarine which would typically be about a third or a 
quarter of the length from the bow. Ignoring transient effects, a vertical force applied at 
point A would cause the submarine to rise or dive while still maintaining level trim. Point 
B moves with changing speed; at very high speed it is almost coincident with point A, but, 
with decreasing speed, it moves aft until, at zero speed, it is infinitely aft of the sub- 
marine. Again, ignoring transient effects, a force applied at point B will cause a submarine 
to change trim but not to change depth. The author did mention that the action of these 
after hydroplanes might be reversed at low speed. This will occur at the speed at which 
point B coincides with the position of the after hydroplanes. At that speed, the after hydro- 
planes can only change the trim and not depth. A downward force applied ahead of point B 
would cause an increase in depth and a downward force applied after point B would cause a 
decrease in depth so that, in passing through the speed at which point B coincides with 
these after hydroplanes, there will be a reversal in the effect on depth of using the planes. 
I would like to suggest to the author that it would be interesting to study, when he has 
the submarine in operation, whether the vertical propeller, which would seem to be almost 
at point A, does in fact control depth without significant effect upon trim, and also to study 
the actual speed, which may well be about 2-1/2 knots, at which the reversal of the after 
hydroplanes’ influence on depth occurs. 
